We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local P\'eclet numbers. A set of numerical tests supports the theoretical derivations.

翻译：我们分析了一种用于线性平流-反应与$p$型扩散（Sobolev指数$p\in(1, \infty)$）问题的间断伽辽金方法。扩散项的离散化基于包含跳跃提升与内部罚函数稳定化的全梯度，而对于平流贡献项，我们考虑了经典迎风格式的强化版本。所推导的误差估计追踪了局部Péclet数对误差局部贡献的依赖性。一系列数值实验验证了理论推导结果。